Abstract

Potts models with a defect line S. Ott and Y. Velenik Preprint (2017). We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the Potts model on $\mathbb{Z}^d$ at temperatures $T>T_c$. We also describe how a line of weakened bonds pins the interface of the Potts model on $\mathbb{Z}^2$ below its critical temperature. These results are obtained by extending the analysis by Friedli, Ioffe and Velenik from Bernoulli percolation to FK-percolation of arbitrary parameter $q>1$. Key words: Potts model, Ising model, FK percolation, random-cluster model, interface, localization, inverse correlation length, coupling constants, pinning, coarse-graining, Ornstein-Zernike asymptotics Files: PDF file, bibtex